光华讲坛——社会名流与企业家论坛第 5778 期
主 题：Testing Mediation Effects Using Logic of Boolean Matrices with Applications in Neuroimaging Mediation Analysis
直播平台及会议ID：腾讯会议，701 322 386
Lexin Li, Ph.D., is Professor of Biostatistics, Department of Biostatistics and Epidemiology, and Helen Wills Neuroscience Institute, University of California, Berkeley. His research interests include neuroimaging analysis, network data analysis, high dimensional regressions, dimension reduction, machine learning, and bioinformatics. He is Fellow of American Statistical Association (ASA), Fellow of Institute of Mathematical Statistics (IMS), and Elected Member of International Statistical Institute (ISI). He has published over 80 peer reviewed articles in statistics and machine learning journals.
Mediation analysis is an important tool in scientific studies such as psychology, genomics, genetic epidemiology, and neuroscience. A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is that the total number of potential paths that go through any mediator is super-exponential in the number of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this talk, we present a new hypothesis testing procedure to evaluate individual mediation effects, while taking into account potential interactions among the mediators. Our key idea is to construct the test statistic using the logic of Boolean matrices, which enables us to establish the proper limiting distribution under the null hypothesis. We further employ screening, data splitting, and decorrelated estimation to reduce the bias and increase the power of the test. We show that our test can control both the size and false discovery rate asymptotically, and the power of the test approaches one, while allowing the number of mediators to diverge to infinity with the sample size. We illustrate our method with two applications in neuroimaging-based mediation analysis for Alzheimer's disease.